2 Answers
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Yes. The iPhone 4 has Bluetooth 2.1 + EDR wireless technology meaning it supports stereo audio and controls. Personally I have these and they have answer/volume +/-/ skip/back/play/pause buttons that all work with iPhone 4.

Older iOS versions had an extremely finicky Bluetooth AVRCP implementation, but since iOS 3 it works reliably with many more devices. The Motorola S9-HD is one of the devices which didn't work well with older iOS, as attested by many reviews; I have one, and while it was indeed flaky under iOS 2, it's been solid ever since iOS 3 came out.